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(c) B. Gerstman 1
Epi Kept Simple
Chapter 3
Epidemiologic Measures
Outline
3.1 Measures of disease frequency
3.2 Measures of association
3.3 Measures of potential impact
3.4 Rate adjustment
mea·sure noun \ˈme-zhər, ˈmā-\Definition of MEASURE1b : the dimensions, capacity, or amount of something ascertained by measuring
3.1 Disease Frequency
• Incidence proportion (risk)
• Incidence rate (incidence density)
• Prevalence
(c) B. Gerstman Chapter 3 3
All are loosely called “rates,” but only the second is a true mathematical rate
Types of Populations
We measure disease frequency in:
• Closed populations “cohorts”
• Open populations
(c) B. Gerstman Chapter 3 4
Closed Population ≡ Cohort
(c) B. Gerstman Chapter 35
Cohort (Latin cohors, meaning “enclosure”; also the basic tactical unit of a Roman legion
Epidemiologic cohort ≡ a group of individuals followed over time
Open Populations • Inflow (immigration,
births) • Outflow (emigration,
death) • An open population
in “steady state” (constant size and age) is said to be stationary
(c) B. Gerstman Chapter 3 6
Numerators & Denominators
• Most measures of disease occurrence are ratios
• Ratios are composed of a numerator and denominator
• Numerator case countIncidence count onsets only
Prevalence count all cases
(c) B. Gerstman Chapter 3 7
Denominators
(c) B. Gerstman Chapter 3 8
Denominators a measure of population size or person-time*
* Person-time ≈ (no. of people) × (time of observation)
Incidence Proportion (IP)
• Synonyms: risk, cumulative incidence, attack rate
• Interpretation: average risk
(c) B. Gerstman Chapter 3 9
Can be calculated in cohorts only
Requires follow-up of individuals
Example: Incidence Proportion (Average Risk)• Objective: estimate the average risk of uterine
cancer in a group• Recruit 1000 women (cohort study)• 100 had hysterectomies, leaving 900 at risk• Follow the cohort for 10 years• Observe 10 new uterine cancer cases
(c) B. Gerstman Chapter 3 10
women900
women10
risk @ no.
onsets of no.IP
10-year average risk is .011 or 1.1%.10-year average risk is .011 or 1.1%.
0111.0
Incidence Rate (IR)
• Synonyms: incidence density, person-time rate
• Interpretation A: “Speed” at which events occur in a population
• Interpretation B: When disease is rare: rate per person-year ≈ one-year average risk
• Calculated differently in closed and open populations
(c) B. Gerstman Chapter 3 11
risk @ time-person of Sum
onsets no.IR
(c) B. Gerstman 12(c) B. Gerstman 12
Example• Objective: estimate rate of uterine cancer• Recruit cohort of 1000 women• 100 had hysterectomies, leaving 900 at risk• Follow at risk individuals for 10 years• Observe 10 onsets of uterine cancer
time-person
onsets of no.IR
Rate is .00111 per year or 11.1 per 10,000 yearsRate is .00111 per year or 11.1 per 10,000 years
years 9000
10
years 10 women900
women10
year
.00111
(c) B. Gerstman 13(c) B. Gerstman 13
Individual follow-up in a Cohort
years 50 years 25
onsets 2
years 75
onsets 2
PY = “person-year”
25 PYs
50 PYs
Incidence Rate, Open Population
(c) B. Gerstman Chapter 3 14
years-person 100,000per 877
nobservatio ofduration size population Avg
onsetsIR
-1year deaths 008770.0
Example: 2,391,630 deaths in 1999 (one year)Population size = 272,705,815
year 1persons 5272,705,81
deaths 2,391,630IR
Prevalence
• Interpretation A: proportion with condition• Interpretation B: probability a person
selected at random will have the condition
(c) B. Gerstman Chapter 3 15
people of no.
cases new and old no.Prevalence
Example: Prevalence of hysterectomy
• Recruit 1000 women
• Ascertain: 100 had hysterectomies
(c) B. Gerstman Chapter 3 16
people of no.
cases no.Prevalence
Prevalence is 10%
10.0people 1000
people 100
Dynamics of PrevalenceCistern Analogy
(c) B. Gerstman Chapter 3 17
Increase incidence increase inflow
Increase average duration of disease decreased outflow
Ways to increase prevalence
Relation Between Incidence and Prevalence
duration) (average rate) (incidence prevalence
(c) B. Gerstman Chapter 3 18
Example: • Incidence rate = 0.01 / year• Average duration of the illness = 2 years. • Prevalence ≈ 0.01 / year × 2 years = 0.02
When disease rare & population stationaryWhen disease rare & population stationary
Gerstman 19
3.2 Measures of Assocation
• Exposure (E) an explanatory factor or potential health determinant; the independent variable
• Disease (D) the response or health-related outcome; the dependent variable
• Measure of association (syn. measure of effect) any statistic that measures the effect on an exposure on the occurrence of an outcome
Gerstman Chapter 8 20
Arithmetic (αριθμός) Comparisons
• Measures of association are mathematical comparisons
• Mathematic comparisons can be done in absolute terms or relative terms
• Let us start with this ridiculously simple example:
• I have $2 • You have $1
"For the things of this world cannot be made known without a knowledge of mathematics."- Roger Bacon
Gerstman Chapter 8 21
Absolute Comparison• In absolute terms, I
have $2 MINUS $1 = $1 more than you
• Note: the absolute comparison was made with subtraction
It is as simple as that…
Gerstman Chapter 8 22
Relative Comparison• Recall that I have $2
and you have $1.
• In relative terms, I have $2 ÷ $1 = 2 times as much as you
• Note: relative comparison was made by division
Gerstman Chapter 8 23
• Suppose, I am exposed to a risk factor and have a 2% risk of disease.
• You are not exposed and you have a 1% risk of the disease.
Absolutes ComparisonsApplied to Risks
• In absolute terms, I have 2% MINUS 1% = 1% greater risk of the disease
• This is the risk difference
Gerstman Chapter 8 24
• In relative terms I have
2% ÷ 1% = 2 twice your risk
• This is the relative risk associated with the exposure
Relative Comparisons Applied to Risks
Gerstman Chapter 8 25
Terminology
For simplicity sake, the terms “risk” and “rate” will be applied to all incidence and prevalence measures.
Gerstman Chapter 8 26
Rate or Risk DifferenceLet RD represent the rate or risk Let RD represent the rate or risk
differencedifference
01 RRRD
where where
RR11 ≡ the risk or rate in the exposed group ≡ the risk or rate in the exposed group
RR00 ≡≡ the risk or rate in the non-exposed risk or rate in the non-exposed groupgroupInterpretation: Interpretation: ExcessExcess risk associated risk associated
with the exposure in absolute termswith the exposure in absolute terms
Gerstman Chapter 8 27
Rate or Risk RatioLet RR represent the rate or risk ratioLet RR represent the rate or risk ratio
0
1
R
RRR
where where
RR11 ≡ the risk or rate in the exposed group ≡ the risk or rate in the exposed group
RR00 ≡≡ the risk or rate in the non-exposed risk or rate in the non-exposed groupgroupInterpretation: excess risk associated Interpretation: excess risk associated with the exposure in relative termswith the exposure in relative terms..
Gerstman 28
Example Fitness & Mortality (Blair et al., 1995)
• Is improved fitness associated with decreased mortality?
• Exposure ≡ improved fitness (1 = yes, 0 = no)
• Disease ≡ death(1 = yes, 0 = no)
• Mortality rate, group 1:R1 = 67.7 per 100,000 PYs
• Mortality rate, group 0:R0 = 122.0 per 100,000 PYs
Gerstman 29
Fitness and Mortality: RD
01 RRRD
The effect of improved fitness was to decrease mortality by 54.4 per 100,000 person-years
Gerstman 30
Example
Relative Risk
0
1
R
RRR 55.0yrs-p 100,000per 0.122
yrs-p 100,000per 7.67
The effect of the improved fitness was to almost cut the rate of death in half.
Gerstman Chapter 8 31
Designation of Exposure• Switching the designation of
“exposure” does not materially affect interpretations
• For example, if we had let “exposure” refer to failure to improve fitness
• RR = R1 / R0 = 122.0 / 67.7 = 1.80 (1.8 times or “almost
twice the rate”)
Gerstman Chapter 8 32
2-by-2 Table FormatDisease + Disease − Total
Exposure + A1 B1 N1
Exposure – A0 B0 N0
Total M1 M0 N
For person-time data: let N1 ≡ person-time in group 1 and N0 ≡ person-time in group 0, and ignore cells B1 and B0
1
11 N
AR
0
00 N
AR
Gerstman Chapter 8 33
Fitness Data, table formatFitness Improved?
Died Person-years
Yes 25 -- 4054
No 32 -- 2937
67.61000,104054
25
1
11
N
AR
95.108000,102937
32
0
00
N
AR
Rates per 10,000 person-years
Gerstman Chapter 8 34
Food borne Outbreak Example
Disease + Disease − Total
Exposure + 63 25 88
Exposure –
1 6 7
Total 64 31 95
7159.088
63
1
11 N
AR 1429.0
7
1
0
00 N
AR
Exposure ≡ eating a particular dishDisease ≡ gastroenteritis
Gerstman Chapter 8 35
Food borne Outbreak Data
71
8863
0
1 R
RRR
1429.0
7159.0 01.5
Exposed group had 5 times the risk
Disease + Disease − Total
Exposure + 63 25 88
Exposure – 1 6 7
Total 64 31 95
Gerstman Chapter 8 37
What do you do when you have multiple levels of exposure?
Compare rates to least exposed “reference” group
LungCA Rate (per 100,000 person-years)
RR
Non-smoker (0) 10 1.0 (ref.)
Light smoker (1) 52 5.2
Mod. smoker (2) 106 10.6
Heavy sm. (3) 224 22.4
2.501
25
0
11
R
RRR 6.10
01
106
0
22 R
RRR
Gerstman Chapter 8 38
The Odds Ratio
• When the disease is rare, interpret the same way you interpret a RR
• e.g. an OR of 1 means the risks are the same in the exposed and nonexposed groups
D+ D− Total
E+ A1 B1 N1
E− A0 B0 N0
Total M1 M0 N
01
01
00
11
AB
BA
BA
BAOR
“Cross-product ratio”
Similar to a RR, but based on odds rather than risks
Gerstman Chapter 8 39
Odds Ratio, ExampleMilunsky et al, 1989, Table 4
NTD = Neural Tube DefectNTD+ NTD−
Folic Acid+ 10 10,703
Folic Acid− 39 11,905
01
01
AB
BAOR
Exposed group had 0.29 times (about a quarter) the risk of the nonexposed group
39703,10
905,1110
29.0
Gerstman Chapter 8 40
Measures of Potential Impact
• These measures predicted impact of removing a hazardous exposure from the population
• Two types– Attributable fraction in
exposed cases– Attributable fraction in
the population as a whole
Gerstman Chapter 8 41
Attributable Fraction Exposed Cases (AFe)
RR
RRAFe
1 :formula Equivalent
1
01 :formula alDefinitionR
RRAFe
Proportion of exposed cases averted with elimination of the exposure
Gerstman Chapter 8 42
Example: AFe
RR of lung CA associated with moderate smoking is approx. 10.4. Therefore:
RR
RRAFe
1
Interpretation: 90.4% of lung cancer in moderate smokers would be averted if they had not smoked.
904.4.10
14.10
Gerstman Chapter 8 43
Attributable Fraction, Population (AFp)
population nonexposedin rate
rate overall
where
:formula alDefinition
0
0
R
R
R
RRAFp
Proportion of all cases averted with elimination of exposure from the population
Gerstman Chapter 8 44
AFp equivalent formulas
populationin exposure of prevalence where
)1(1
)1(
e
e
ep
p
RRp
RRpAF
exposed are that cases of proportion where
c
cep
p
pAFAF
Gerstman Chapter 8 45
AFp for Cancer Mortality, Selected Exposures
Exposure Doll & Peto, 1981 Miller, 1992
Tobacco 30% 29%
Dietary 35% 20%
Occupational 4% 9%
Repro/Sexual 7% 7%
Sun/Radiation 3% 1%
Alcohol 3% 6%
Pollution 2% -
Medication 1% 2%
Infection 10% -
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